The Treasury is considering whether to make changes to its controversial new banking tax after extensive lobbying from ‘challenger banks’.

Banks such as Metro and Secure Trust met Treasury officials on Friday amid continued controversy about the new tax introduced in July’s budget. Banks will be required to pay an extra 8% of corporation tax on profits of more than £25m from next year, following a decision by George Osborne to water down the bank levy which is calculated on the size of balance sheets rather than profits.

There are concerns that the 8% surcharge could stifle competition as it will leave smaller banks with a higher tax bill, while the big banks with an international presence such as HSBC are expected to be pay less overall because of the cut to the bank levy.

Paul Lynam, chief executive of Secure Trust and chair of the British Bankers’ Association’s challenger bank panel, said: “We are not willing let to let this drop and think it’s hugely important to the UK economy.”

No further meetings have been scheduled between the smaller banks and Treasury officials, although they are thought to have agreed to consider whether the new tax could have a tiered structure. However no changes are likely to be imminent.

The challenger banks had argued that to create fairer competition with the established players there needed to be a change to rules covering the amount of capital they hold and the way they access funds through programmes such as the Bank of England’s funding for lending scheme.

The Treasury said the tax regime for banks was “sustainable and fair”.

“While Britain is host to some of the largest and most successful banks on the planet, the government has been consistently clear it wants to see a more vibrant and competitive banking sector with new banks and more innovation, benefiting working people and businesses,” the Treasury said.

The finance bill, which implemented the tax measures, has passed through parliament without any changes.

The government has said it wants to encourage competition in the banking sector to break the dominance of the big four of HSBC, Barclays, and bailed out banks Lloyds Banking Group and Royal Bank of Scotland.